Is this sentiment remotely presidential?
Yes, by definition, since "presidential" doesn't really mean anything besides "of or relating to the president" and Trump is the president.
Thus everything he says is presidential.
"presidential" is a made up thing, no one ever says that this or that is "presidential" besides Lincoln Towncars and hotel suites they always say that whenever it is a president is doing or saying is something they don't like then they say is "not presidential". If you are upset by the president but what he is doing is perfectly legal and you can't think of any legitimate criticism then they say "that's not presidential!"
As president, he vowed to uphold the constitution, which includes the first amendment and the ability to voice unpopular opinions in non-violent ways.
Yes he did, and what a great job he does, his tweet is an example of doing that, Trump leads by example. Trump has a right to express unpopular ideas doesn't he?
Should the president, who represents the government, share an idea that could be remotely construed as opposing free expression?
The president can and should share any idea he wants, he has freedom of speech. Hillary Clinton called to do away with the 1st Amendment by amending the constitution, did you have a problem with that?
She is free to call for that isn't she? Is she won she could still call for that right?
In fact the reason that people wanted him to be president was so that he would be heard. Moreoever it's pretty insane, especially at this point, to blame Donald Trump for the media intentionally misconstruing things he says. Should Trump say nothing? Do you really think he is responsible for being intentionally misconstrued by the media?
If Trump said "I hate injustice" they would run a headline that Trump said "I hate". Did you see this NYT article? He said MS 13 members are animals and they said he called immigrants animals.
RE: Trump: "Players Who Don't Stand For The Anthem Shouldn't Be In The Country"